Polar Form Calculator
Convert a complex number from rectangular form a + bi to magnitude-and-phase form using the quadrant-aware argument.
Magnitude: 5.000000
Phase: 0.927295 rad
Input: 3.000000 + 4.000000i
Rectangular form a + bi
Required. Use a decimal point; commas are rejected. Scientific notation such as 1e3 is accepted.
Required. Enter the coefficient of i, including its sign.
Polar form r × exp(iφ)
Polar form
5.000000 × exp(i0.927295)
Magnitude (r)
5.000000
Phase (φ)
0.927295 rad
Magnitude 5.000000. Phase 0.927295 radians.
Calculation details
| Quantity | Formula | Value |
|---|---|---|
| Real part | a | 3.000000 |
| Imaginary part | b | 4.000000 |
| Squared real part | a² | 9.000000 |
| Squared imaginary part | b² | 16.000000 |
| Sum of squares | a² + b² | 25.000000 |
| Magnitude | √(a² + b²) | 5.000000 |
| Phase | atan2(b, a) | 0.927295 rad |
The phase is the principal argument in the interval ( – π, π